Quagliarella is looking to rejuvenate his career after a frustrating spell at Juventus where he has regularly warmed the bench.
The 2006 World Cup winner has made clear his intention to find first-team football and has no realistic chance of breaking up the lethal partnership of Carlos Tevez and Fernando Llorente.
West Brom were amongst the clubs who considered signing Quagliarella on loan in January when he also nearly joined Tottenham and Cardiff City but ultimately stayed put.
Parma may have a significant advantage because they have qualified for next season's Europa League, but that could be negated as the Ducali are at risk of losing their place due to unpaid taxes.
Much will depend on Quagliarella's feelings about playing abroad. It was suggested that his reluctance to move in January was due to a desire to stay within Italy.
Juventus will be keen to let Quagliarella leave to make space for new arrivals and could be open to a reduced offer for the player, whose contract expires in 2015.